Dissipative control and filtering of discrete-time singular systems

In this paper, the problems of dissipative control and filtering of discrete-time singular systems are investigated. Based on parametrising the solutions of the constraint set, a necessary and sufficient condition is established in terms of strict linear matrix inequality which makes the condition more tractable. By using the system augmentation approach, a static output feedback controller design method is proposed to guarantee that the closed-loop system is admissible and strictly (Q, S, R) dissipative. Then, the result is applied to tackle the reduced-order filtering problem. The effectiveness of the obtained results in this paper is illustrated by numerical examples.

[1]  Hui Li,et al.  Quantized H∞ Filtering for Singular Time-varying Delay Systems with Unreliable Communication Channel , 2012, Circuits Syst. Signal Process..

[2]  Chunyu Yang,et al.  Positive Realness and Absolute Stability Problem of Descriptor Systems , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[3]  Shengyuan Xu,et al.  H∞ filtering for singular systems , 2003, IEEE Trans. Autom. Control..

[4]  Shengyuan Xu,et al.  H∞ model reduction for discrete-time singular systems , 2003, Syst. Control. Lett..

[5]  Xin-zhuang Dong.  Robust strictly dissipative control for discrete singular systems , 2007 .

[6]  M. Perrier,et al.  Hα filtering for discrete-time affine non-linear descriptor systems , 2012 .

[7]  Minyue Fu,et al.  Reduced-order H ∞ filtering for discrete-time singular systems with lossy measurements , 2010 .

[8]  C. Yung.  H∞ Control for Linear Discrete-Time Descriptor Systems: State Feedback and Full Information Cases , 2008 .

[9]  Chengwu Yang,et al.  H∞ state feedback control for discrete singular systems , 2000, IEEE Trans. Autom. Control..

[10]  Shengyuan Xu,et al.  Reduced-order H∞ filtering for singular systems , 2007, Syst. Control. Lett..

[11]  James Lam,et al.  An augmented system approach to static output‐feedback stabilization with ℋ︁∞ performance for continuous‐time plants , 2009 .

[12]  Izumi Masubuchi,et al.  Dissipativity inequalities for continuous-time descriptor systems with applications to synthesis of control gains , 2006, Syst. Control. Lett..

[13]  Junpeng Li,et al.  Reduced-order L 2 -L ∞ filtering for singular systems: a linear matrix inequality approach , 2008 .

[14]  James Lam,et al.  α-Dissipativity analysis of singular time-delay systems , 2011, Autom..

[15]  R. Newcomb.  The semistate description of nonlinear time-variable circuits , 1981 .

[16]  Juan Zhou,et al.  Dissipative control for a class of nonlinear descriptor systems , 2016, Int. J. Syst. Sci..

[17]  Jong-Hae Kim,et al.  Delay-dependent robust Hinfinity filtering for uncertain discrete-time singular systems with interval time-varying delay , 2010, Autom..

[18]  James Lam,et al.  Robust reliable dissipative filtering for discrete delay singular systems , 2012, Signal Process..

[19]  Timo Reis,et al.  H∞-control for descriptor systems - A structured matrix pencils approach , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[20]  Izumi Masubuchi,et al.  PII: S0005-1098(96)00193-8 , 2003 .

[21]  Jian-xun Li,et al.  Energy-to-peak filtering for singular systems: the discrete-time case , 2008 .

[22]  P. Daoutidis,et al.  Feedback control of nonlinear differential-algebraic-equation systems , 1995 .

[23]  X. Xu,et al.  Impulsive control in continuous and discrete-continuous systems [Book Reviews] , 2003, IEEE Transactions on Automatic Control.

[24]  James Lam,et al.  $H_{\infty}$ Positive Filtering for Positive Linear Discrete-Time Systems: An Augmentation Approach , 2010, IEEE Transactions on Automatic Control.

[25]  Bin Zhou,et al.  Brief paper: Strict linear matrix inequality characterisation of positive realness for linear discrete-time descriptor systems , 2010 .

[26]  Yueying Wang,et al.  Exponential $H_{\infty}$ Filtering for Singular Markovian Jump Systems With Mixed Mode-Dependent Time-Varying Delay , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  Jong Hae Kim.  Reduced-order delay-dependent H∞ filtering for uncertain discrete-time singular systems with time-varying delay , 2011, Autom..

[28]  J. Löfberg.  Modeling and solving uncertain optimization problems in YALMIP , 2008 .

[29]  Renquan Lu,et al.  H∞ filtering for singular systems with communication delays , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[30]  Louis R. Hunt,et al.  Finding maximum linear subsystems of nonlinear systems with outputs , 2000, IEEE Trans. Autom. Control..

[31]  Ju H. Park,et al.  Dissipativity analysis for singular systems with time-varying delays , 2011, Appl. Math. Comput..

[32]  Strictly passive static output feedback control for discrete singular system , 2010, 2010 8th World Congress on Intelligent Control and Automation.

[33]  P. Chevrel,et al.  On dissipativity of continues-time singular systems , 2010, 18th Mediterranean Conference on Control and Automation, MED'10.

[34]  Cheng-Kok Koh,et al.  Passivity Enforcement for Descriptor Systems Via Matrix Pencil Perturbation , 2012, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[35]  James Lam,et al.  Reduced-order dissipative filtering for discrete-time singular systems , 2013, 2013 IEEE International Symposium on Industrial Electronics.

[36]  Mohamed Darouach,et al.  Novel bounded real lemma for discrete-time descriptor systems: Application to H∞ control design , 2012, Autom..

[37]  E. Boukas,et al.  Delay-Dependent Stability Analysis of Singular Linear Continuous-time System , 2003, 2003 4th International Conference on Control and Automation Proceedings.

[38]  Xiaozhan Yang,et al.  Dissipativity Analysis and Synthesis for Discrete-Time T–S Fuzzy Stochastic SystemsWith Time-Varying Delay , 2014, IEEE Transactions on Fuzzy Systems.

[39]  Zhengguang Wu,et al.  H∞ filtering for discrete-time singular systems with randomly occurring delays and sensor failures , 2012 .

[40]  Izumi Masubuchi.  Output feedback controller synthesis for descriptor systems satisfying closed-loop dissipativity , 2007, Autom..

[41]  J. Tsitsiklis,et al.  NP-hardness of some linear control design problems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[42]  Renquan Lu,et al.  A simple approach to robust D‐stability analysis for uncertain singular delay systems , 2009 .

[43]  Guoliang Wang,et al.  Dissipative control for singular Markovian jump systems with time delay , 2012 .

[44]  J. Bernussou,et al.  A new robust D-stability condition for real convex polytopic uncertainty , 2000 .

[45]  Hongye Su,et al.  Delay-dependent H∞ filtering for singular Markovian jump time-delay systems , 2010, Signal Process..

[46]  Shengyuan Xu,et al.  Robust Control and Filtering of Singular Systems , 2006 .

[47]  A Strict LMI Condition for ESPR Property of Continuous-Time Descriptor Systems , 2007 .

[48]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[49]  Yuanqing Xia,et al.  New bounded real lemma for discrete-time singular systems , 2008, Autom..

[50]  Qingling Zhang,et al.  Model reduction of singular systems via covariance approximation , 2004, Proceedings of the 2004 American Control Conference.

[51]  Yuan-Yuan Chen,et al.  Static output feedback stabilization for discrete singular large-scale control systems , 2010, 2010 International Conference on Machine Learning and Cybernetics.

[52]  Kan-Lin Hsiung,et al.  Lyapunov inequality and bounded real lemma for discrete-time descriptor systems , 1999 .

[53]  James Lam,et al.  Stability and Dissipativity Analysis of Distributed Delay Cellular Neural Networks , 2011, IEEE Transactions on Neural Networks.

[54]  L. Lee,et al.  Strictly positive real lemma and absolute stability for discrete-time descriptor systems , 2003 .

[55]  D. Luenberger,et al.  SINGULAR DYNAMIC LEONTIEF SYSTEMS1 , 1977 .

[56]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .